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      <h1 class="mume-header" id="zuc%E7%A5%96%E5%86%B2%E4%B9%8B%E5%BA%8F%E5%88%97%E5%AF%86%E7%A0%81%E7%AE%97%E6%B3%95">ZUC&#x7956;&#x51B2;&#x4E4B;&#x5E8F;&#x5217;&#x5BC6;&#x7801;&#x7B97;&#x6CD5;</h1>

<p><a href="https://crates.io/crates/rcrypto">Rust&#x5B9E;&#x73B0;</a>;</p>
<p><span id="toc"></span></p>
<ul>
<li><a href="#zuc%E7%A5%96%E5%86%B2%E4%B9%8B%E5%BA%8F%E5%88%97%E5%AF%86%E7%A0%81%E7%AE%97%E6%B3%95">ZUC&#x7956;&#x51B2;&#x4E4B;&#x5E8F;&#x5217;&#x5BC6;&#x7801;&#x7B97;&#x6CD5;</a>
<ul>
<li><a href="#zuc%E7%AE%97%E6%B3%95%E6%A6%82%E8%A6%81toc">ZUC&#x7B97;&#x6CD5;&#x6982;&#x8981;</a>
<ul>
<li><a href="#lfsr%E7%BA%BF%E6%80%A7%E5%8F%8D%E9%A6%88%E7%A7%BB%E4%BD%8D%E5%AF%84%E5%AD%98%E5%99%A8toc">LFSR&#x7EBF;&#x6027;&#x53CD;&#x9988;&#x79FB;&#x4F4D;&#x5BC4;&#x5B58;&#x5668;</a>
<ul>
<li><a href="#lfsr%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A8%A1%E5%BC%8Ftoc">LFSR&#x521D;&#x59CB;&#x5316;&#x6A21;&#x5F0F;</a></li>
<li><a href="#lfsr%E5%B7%A5%E4%BD%9C%E6%A8%A1%E5%BC%8Ftoc">LFSR&#x5DE5;&#x4F5C;&#x6A21;&#x5F0F;</a></li>
</ul>
</li>
<li><a href="#br%E6%AF%94%E7%89%B9%E9%87%8D%E7%BB%84toc">BR&#x6BD4;&#x7279;&#x91CD;&#x7EC4;</a></li>
<li><a href="#f%E9%9D%9E%E7%BA%BF%E6%80%A7%E5%87%BD%E6%95%B0toc">F&#x975E;&#x7EBF;&#x6027;&#x51FD;&#x6570;</a></li>
<li><a href="#%E5%AF%86%E9%92%A5%E8%A3%85%E5%85%A5toc">&#x5BC6;&#x94A5;&#x88C5;&#x5165;</a></li>
</ul>
</li>
<li><a href="#%E5%9F%BA%E4%BA%8Ezuc%E7%9A%84%E5%8A%A0%E5%AF%86%E7%AE%97%E6%B3%95toc">&#x57FA;&#x4E8E;ZUC&#x7684;&#x52A0;&#x5BC6;&#x7B97;&#x6CD5;</a>
<ul>
<li><a href="#zuccipher%E7%AE%97%E6%B3%95%E6%8F%8F%E8%BF%B0toc">ZUCCipher&#x7B97;&#x6CD5;&#x63CF;&#x8FF0;</a></li>
<li><a href="#zuccipher%E5%88%9D%E5%A7%8B%E5%8C%96toc">ZUCCipher&#x521D;&#x59CB;&#x5316;</a></li>
<li><a href="#zuccipher%E5%AF%86%E9%92%A5%E6%B5%81%E7%94%9F%E6%88%90toc">ZUCCipher&#x5BC6;&#x94A5;&#x6D41;&#x751F;&#x6210;</a></li>
<li><a href="#zuccipher%E5%8A%A0%E8%A7%A3%E5%AF%86toc">ZUCCipher&#x52A0;&#x89E3;&#x5BC6;</a></li>
</ul>
</li>
<li><a href="#%E5%9F%BA%E4%BA%8Ezuc%E7%9A%84%E6%B6%88%E6%81%AF%E8%AE%A4%E8%AF%81%E7%AE%97%E6%B3%95toc">&#x57FA;&#x4E8E;ZUC&#x7684;&#x6D88;&#x606F;&#x8BA4;&#x8BC1;&#x7B97;&#x6CD5;</a>
<ul>
<li><a href="#zucmac%E7%AE%97%E6%B3%95%E6%8F%8F%E8%BF%B0toc">ZUCMac&#x7B97;&#x6CD5;&#x63CF;&#x8FF0;</a></li>
<li><a href="#zucmac%E5%88%9D%E5%A7%8B%E5%8C%96toc">ZUCMac&#x521D;&#x59CB;&#x5316;</a></li>
<li><a href="#zucmac%E5%AF%86%E9%92%A5%E6%B5%81%E7%94%9F%E6%88%90toc">ZUCMac&#x5BC6;&#x94A5;&#x6D41;&#x751F;&#x6210;</a></li>
<li><a href="#zucmac%E6%B6%88%E6%81%AF%E8%AE%A4%E8%AF%81%E7%A0%81%E7%94%9F%E6%88%90toc">ZUCMac&#x6D88;&#x606F;&#x8BA4;&#x8BC1;&#x7801;&#x751F;&#x6210;</a></li>
</ul>
</li>
<li><a href="#%E9%99%84%E5%BD%95toc">&#x9644;&#x5F55;</a>
<ul>
<li><a href="#%E8%AF%B4%E6%98%8Etoc">&#x8BF4;&#x660E;</a></li>
<li><a href="#s_0-s_1toc"><span class="mathjax-exps">$S_0, S_1$</span></a></li>
<li><a href="#kdtoc">KD</a></li>
</ul>
</li>
<li><a href="#%E5%8F%82%E8%80%83%E8%B5%84%E6%96%99">&#x53C2;&#x8003;&#x8D44;&#x6599;</a></li>
</ul>
</li>
</ul>
<h2 class="mume-header" id="zuc%E7%AE%97%E6%B3%95%E6%A6%82%E8%A6%81toc"><a href="#toc">ZUC&#x7B97;&#x6CD5;&#x6982;&#x8981;</a></h2>

<p>ZUC&#x4E3B;&#x8981;&#x7531;LFSR&#x7EBF;&#x6027;&#x53CD;&#x9988;&#x79FB;&#x4F4D;&#x5BC4;&#x5B58;&#x5668;, BR&#x6BD4;&#x7279;&#x91CD;&#x7EC4;&#x548C;F&#x975E;&#x7EBF;&#x6027;&#x51FD;&#x6570;&#x4E09;&#x90E8;&#x5206;&#x7EC4;&#x6210;;</p>
<ul>
<li>&#x8F93;&#x5165;: 128&#x4F4D;&#x957F;&#x7684;&#x5BC6;&#x94A5;, 128&#x4F4D;&#x957F;&#x7684;&#x521D;&#x59CB;&#x5316;&#x5411;&#x91CF;;</li>
<li>&#x8F93;&#x51FA;: <span class="mathjax-exps">$n, n \in N^+$</span>&#x4E2A;32&#x4F4D;&#x957F;&#x7684;&#x5B57;&#x4E32;, <span class="mathjax-exps">$n$</span>&#x4E3A;&#x8282;&#x62CD;&#x6570;(&#x8F6E;&#x6570;);</li>
<li>&#x7B97;&#x6CD5;&#x8FC7;&#x7A0B;<code>ZUC(KEY, IV, n)</code>:
<ul>
<li>&#x521D;&#x59CB;&#x5316;&#x9636;&#x6BB5;:
<ul>
<li><code>for i in 0..32</code>:<br>
-<code>BitReconstruction()</code>;
<ul>
<li><code>W = F(X_0, X_1, X_2)</code>;</li>
<li><code>LFSRWithInitializationMode(W &gt;&gt; 1)</code>;</li>
</ul>
</li>
</ul>
</li>
<li>&#x5DE5;&#x4F5C;&#x9636;&#x6BB5;:
<ul>
<li><code>BitReconstruction()</code>;</li>
<li><code>F(X_0, X_1, X_2)</code>;</li>
<li><code>LFSRWithWorkMode()</code>;</li>
<li><code>for i in 0..n</code>:
<ul>
<li><code>BitReconstruction()</code>;</li>
<li><code>z_i = F(X_0, X_1, X_2) ^ X_3</code>;</li>
<li><code>LFSRWithWorkMode()</code>;</li>
</ul>
</li>
<li><span class="mathjax-exps">$z_0||z_1||z_2||z_3$</span>;</li>
</ul>
</li>
</ul>
</li>
</ul>
<h3 class="mume-header" id="lfsr%E7%BA%BF%E6%80%A7%E5%8F%8D%E9%A6%88%E7%A7%BB%E4%BD%8D%E5%AF%84%E5%AD%98%E5%99%A8toc"><a href="#toc">LFSR&#x7EBF;&#x6027;&#x53CD;&#x9988;&#x79FB;&#x4F4D;&#x5BC4;&#x5B58;&#x5668;</a></h3>

<ul>
<li><span class="mathjax-exps">$s_0, s_1, \dots, s_{15}$</span>&#x4E3A;LFSR&#x7684;16&#x4E2A;31&#x4F4D;&#x957F;&#x7684;&#x5BC4;&#x5B58;&#x5668;;</li>
</ul>
<h4 class="mume-header" id="lfsr%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A8%A1%E5%BC%8Ftoc"><a href="#toc">LFSR&#x521D;&#x59CB;&#x5316;&#x6A21;&#x5F0F;</a></h4>

<ul>
<li><code>LFSRWithInitilizationMode(u)</code>:
<ul>
<li><span class="mathjax-exps">$v=2^{15} s_{15} + 2^{17} s_{13} + 2^{21}s_{10} + 2^{20}s_{4}+(1+2^8)s_0 \mod (2^{31}-1)$</span>;</li>
<li><span class="mathjax-exps">$s_{16} = (v + u)\mod (2^{31} - 1)$</span>;</li>
<li>if <span class="mathjax-exps">$s_{16} = 0$</span>:
<ul>
<li><span class="mathjax-exps">$s_{16} = 2^{31} - 1$</span>;</li>
</ul>
</li>
<li><span class="mathjax-exps">$s_0, s_1, \dots, s_{15} = s_1, s_2,\dots, s_{16}$</span></li>
</ul>
</li>
</ul>
<h4 class="mume-header" id="lfsr%E5%B7%A5%E4%BD%9C%E6%A8%A1%E5%BC%8Ftoc"><a href="#toc">LFSR&#x5DE5;&#x4F5C;&#x6A21;&#x5F0F;</a></h4>

<ul>
<li><code>LFSRWithWorkMode(u)</code>:
<ul>
<li><span class="mathjax-exps">$s_{16}=2^{15} s_{15} + 2^{17} s_{13} + 2^{21}s_{10} + 2^{20}s_{4}+(1+2^8)s_0 \mod (2^{31}-1)$</span>;</li>
<li>if <span class="mathjax-exps">$s_{16} = 0$</span>:
<ul>
<li><span class="mathjax-exps">$s_{16} = 2^{31} - 1$</span>;</li>
</ul>
</li>
<li><span class="mathjax-exps">$s_0, s_1, \dots, s_{15} = s_1, s_2,\dots, s_{16}$</span></li>
</ul>
</li>
</ul>
<h3 class="mume-header" id="br%E6%AF%94%E7%89%B9%E9%87%8D%E7%BB%84toc"><a href="#toc">BR&#x6BD4;&#x7279;&#x91CD;&#x7EC4;</a></h3>

<ul>
<li><code>BitReconstruction()</code>:
<ul>
<li><span class="mathjax-exps">$X_0 = (s_{15} \land 0xffff0000) \lor (s_{14} \land 0x0000ffff)$</span>;</li>
<li><span class="mathjax-exps">$X_1 = (s_{9} \land 0xffff0000) \lor (s_{11} \land 0x0000ffff)$</span>;</li>
<li><span class="mathjax-exps">$X_2 = (s_{5} \land 0xffff0000) \lor (s_{7} \land 0x0000ffff)$</span>;</li>
<li><span class="mathjax-exps">$X_3 = (s_{0} \land 0xffff0000) \lor (s_{2} \land 0x0000ffff)$</span>;</li>
</ul>
</li>
</ul>
<h3 class="mume-header" id="f%E9%9D%9E%E7%BA%BF%E6%80%A7%E5%87%BD%E6%95%B0toc"><a href="#toc">F&#x975E;&#x7EBF;&#x6027;&#x51FD;&#x6570;</a></h3>

<ul>
<li>
<p><code>F(X_0, X_1, X_2)</code>:</p>
<ul>
<li><span class="mathjax-exps">$W = (X_0 \oplus R_1) + R_2 \mod 2^{32}$</span>;</li>
<li><span class="mathjax-exps">$W_1 = R_1 + X_1 \mod 2^{32}$</span>;</li>
<li><span class="mathjax-exps">$W_2 = R_2 \oplus X_2$</span>;;</li>
<li><span class="mathjax-exps">$R_1 = S(L_1((W_1 \land 0x0000ffff) \lor (W_2 \land 0xffff0000)))$</span>;</li>
<li><span class="mathjax-exps">$R_2 = S(L_2((W_2 \land 0x0000ffff) \lor (W_1 \land 0xffff0000)))$</span>;</li>
<li>&#x8F93;&#x51FA;<span class="mathjax-exps">$W$</span>;</li>
</ul>
</li>
<li>
<p><code>L_1(X)</code>:</p>
<ul>
<li><span class="mathjax-exps">$X\oplus (X \lll 2) \oplus (X\lll 10) \oplus (X \lll 18) \oplus (X \lll 24)$</span>;</li>
</ul>
</li>
<li>
<p><code>L_2(X)</code>:</p>
<ul>
<li><span class="mathjax-exps">$X\oplus (X \lll 8) \oplus (X\lll 14) \oplus (X \lll 22) \oplus (X\lll 30)$</span>;</li>
</ul>
</li>
<li>
<p><code>S(X)</code>:</p>
<ul>
<li><span class="mathjax-exps">$S_0, S_1$</span>&#x662F;&#x4E00;&#x4E2A;&#x5927;&#x5C0F;&#x4E3A;256&#x7684;&#x5143;&#x7D20;&#x4E3A;&#x5B57;&#x8282;&#x7684;&#x5E38;&#x91CF;&#x8868;, &#x89C1;&#x9644;&#x5F55;;</li>
<li><span class="mathjax-exps">$X = x_0 || x_1 || x_2 || x_3, bitslen(x_0)=bitslen(x_1)=bitslen(x_2)=bitslen(x_3)=8$</span>;</li>
<li><span class="mathjax-exps">$y_0=S_0[x_0]$</span>;</li>
<li><span class="mathjax-exps">$y_1=S_1[x_1]$</span>;</li>
<li><span class="mathjax-exps">$y_2=S_0[x_2]$</span>;</li>
<li><span class="mathjax-exps">$y_3=S_1[x_3]$</span>;</li>
<li><span class="mathjax-exps">$y_0 || y_1 || y_2 || y_3$</span>;</li>
</ul>
</li>
</ul>
<h3 class="mume-header" id="%E5%AF%86%E9%92%A5%E8%A3%85%E5%85%A5toc"><a href="#toc">&#x5BC6;&#x94A5;&#x88C5;&#x5165;</a></h3>

<p>&#x5BC6;&#x94A5;&#x88C5;&#x5165;&#x662F;&#x5C06;128&#x4F4D;&#x957F;&#x7684;&#x5BC6;&#x94A5;<span class="mathjax-exps">$K$</span>&#x548C;128&#x4F4D;&#x957F;&#x7684;&#x521D;&#x59CB;&#x5411;&#x91CF;<span class="mathjax-exps">$IV$</span>&#x6269;&#x5C55;&#x4E3A;16&#x4E2A;31&#x4F4D;&#x957F;&#x7684;&#x5B57;, &#x5E76;&#x653E;&#x5165;LFSR&#x7684;16&#x4E2A;&#x5BC4;&#x5B58;&#x5668;<span class="mathjax-exps">$s_0,s_1,\dots,s_{15}$</span>&#x4E2D;&#x7684;&#x8FC7;&#x7A0B;.</p>
<ul>
<li><code>KeySchedule(K, IV)</code>:
<ul>
<li>&#x5C06;<span class="mathjax-exps">$K$</span>&#x548C;<span class="mathjax-exps">$IV$</span>&#x5212;&#x5206;&#x4E3A;16&#x4E2A;&#x5747;&#x7B49;&#x957F;&#x5EA6;&#x7684;8&#x4F4D;&#x957F;&#x7684;&#x5B57;&#x8282;;
<ul>
<li><span class="mathjax-exps">$K = k_0 || k_1 || \dots || k_{15}$</span>;</li>
<li><span class="mathjax-exps">$IV = iv_0 || iv_1 || \dots || iv_{15}$</span>;</li>
</ul>
</li>
<li><span class="mathjax-exps">$s_i = k_i || rightmost_{15}(KD[i]) || iv_i$</span>, <span class="mathjax-exps">$KD$</span>&#x662F;&#x5927;&#x5C0F;&#x4E3A;16&#x7684;&#x5143;&#x7D20;&#x4E3A;16&#x4F4D;&#x957F;&#x5EA6;&#x7684;&#x5E38;&#x91CF;&#x8868;(&#x89C1;&#x9644;&#x5F55;), <span class="mathjax-exps">$rightmost_l(x)$</span>&#x8868;&#x793A;&#x53D6;<span class="mathjax-exps">$x$</span>&#x7684;&#x6700;&#x53F3;&#x8FB9;<span class="mathjax-exps">$l$</span>&#x4F4D;&#x6BD4;&#x7279;&#x4F4D;;</li>
</ul>
</li>
</ul>
<h2 class="mume-header" id="%E5%9F%BA%E4%BA%8Ezuc%E7%9A%84%E5%8A%A0%E5%AF%86%E7%AE%97%E6%B3%95toc"><a href="#toc">&#x57FA;&#x4E8E;ZUC&#x7684;&#x52A0;&#x5BC6;&#x7B97;&#x6CD5;</a></h2>

<h3 class="mume-header" id="zuccipher%E7%AE%97%E6%B3%95%E6%8F%8F%E8%BF%B0toc"><a href="#toc">ZUCCipher&#x7B97;&#x6CD5;&#x63CF;&#x8FF0;</a></h3>

<table>
<thead>
<tr>
<th style="text-align:center">&#x8F93;&#x5165;&#x53C2;&#x6570;</th>
<th style="text-align:center">&#x4F4D;&#x957F;&#x5EA6;</th>
<th style="text-align:center">&#x9644;&#x6CE8;</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">COUNT</td>
<td style="text-align:center">32</td>
<td style="text-align:center">&#x8BA1;&#x6570;&#x5668;</td>
</tr>
<tr>
<td style="text-align:center">BEARER</td>
<td style="text-align:center">5</td>
<td style="text-align:center">&#x627F;&#x8F7D;&#x5C42;&#x6807;&#x8BC6;</td>
</tr>
<tr>
<td style="text-align:center">DIRECTION</td>
<td style="text-align:center">1</td>
<td style="text-align:center">&#x4F20;&#x8F93;&#x65B9;&#x5411;&#x6807;&#x8BC6;</td>
</tr>
<tr>
<td style="text-align:center">CK</td>
<td style="text-align:center">128</td>
<td style="text-align:center">&#x5BC6;&#x94A5;</td>
</tr>
<tr>
<td style="text-align:center">LENGTH</td>
<td style="text-align:center">32</td>
<td style="text-align:center">&#x660E;&#x6587;&#x6D88;&#x606F;&#x6D41;&#x7684;&#x4F4D;&#x957F;&#x5EA6;</td>
</tr>
<tr>
<td style="text-align:center">IBS</td>
<td style="text-align:center">LENGTH</td>
<td style="text-align:center">&#x8F93;&#x5165;&#x6BD4;&#x7279;&#x6D41;</td>
</tr>
</tbody>
</table>
<table>
<thead>
<tr>
<th style="text-align:center">&#x8F93;&#x51FA;&#x53C2;&#x6570;</th>
<th style="text-align:center">&#x4F4D;&#x957F;&#x5EA6;</th>
<th style="text-align:center">&#x9644;&#x6CE8;</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">OBS</td>
<td style="text-align:center">LENGTH</td>
<td style="text-align:center">&#x8F93;&#x51FA;&#x6BD4;&#x7279;&#x6D41;</td>
</tr>
</tbody>
</table>
<h3 class="mume-header" id="zuccipher%E5%88%9D%E5%A7%8B%E5%8C%96toc"><a href="#toc">ZUCCipher&#x521D;&#x59CB;&#x5316;</a></h3>

<ul>
<li><span class="mathjax-exps">$CK = CK[0] || CK[1] || \dots || CK[15], bitslen(CK[i])=8, i \in [0,15]$</span>;</li>
<li><span class="mathjax-exps">$KEY[i] = CK[i], i\in [0, 15]$</span>;</li>
<li><span class="mathjax-exps">$COUNT = COUNT[0] || COUNT[1] || COUNT[2] || COUNT[3], bitslen(COUNT[i])=8, i \in [0,3]$</span>;</li>
<li><span class="mathjax-exps">$IV = IV[0] || IV[1] ||\dots || IV[15], bitslen(IV[i])=8, i\in [0,15]$</span>;</li>
<li><span class="mathjax-exps">$IV[i] = COUNT[i], i = 0\dots 3$</span>;</li>
<li><span class="mathjax-exps">$IV[4] = BEARER || DIRECTION || 0 || 0$</span>;</li>
<li><span class="mathjax-exps">$IV[5]=IV[6] = IV[7] = 0x00$</span>;</li>
<li><span class="mathjax-exps">$IV[j+8] = IV[j], j\in [0,7]$</span>;</li>
</ul>
<h3 class="mume-header" id="zuccipher%E5%AF%86%E9%92%A5%E6%B5%81%E7%94%9F%E6%88%90toc"><a href="#toc">ZUCCipher&#x5BC6;&#x94A5;&#x6D41;&#x751F;&#x6210;</a></h3>

<ul>
<li><span class="mathjax-exps">$n= \lceil LENGTH / 32 \rceil$</span>;</li>
<li><span class="mathjax-exps">$K&apos; = ZUC(KEY,IV,n)$</span>;</li>
<li><span class="mathjax-exps">$K&apos; = k_0 || k_1 || \dots || K_{32\cdot n - 1}, bitslen(k_i)=1, i\in [0, 32\cdot n - 1]$</span>;</li>
</ul>
<h3 class="mume-header" id="zuccipher%E5%8A%A0%E8%A7%A3%E5%AF%86toc"><a href="#toc">ZUCCipher&#x52A0;&#x89E3;&#x5BC6;</a></h3>

<ul>
<li><span class="mathjax-exps">$IBS = IBS[0]||IBS[1]||\dots ||IBS[LENGTH], bitslen(IBS[i])=1, i\in [0,LENGTH-1]$</span>;</li>
<li><span class="mathjax-exps">$OBS[i] = ISB[i]\oplus k_i, i\in [0,LENGTH-1]$</span>;</li>
<li><span class="mathjax-exps">$OBS = OBS[0]||OBS[1]||\dots || OBS[LENGTH-1]$</span>;</li>
</ul>
<h2 class="mume-header" id="%E5%9F%BA%E4%BA%8Ezuc%E7%9A%84%E6%B6%88%E6%81%AF%E8%AE%A4%E8%AF%81%E7%AE%97%E6%B3%95toc"><a href="#toc">&#x57FA;&#x4E8E;ZUC&#x7684;&#x6D88;&#x606F;&#x8BA4;&#x8BC1;&#x7B97;&#x6CD5;</a></h2>

<h3 class="mume-header" id="zucmac%E7%AE%97%E6%B3%95%E6%8F%8F%E8%BF%B0toc"><a href="#toc">ZUCMac&#x7B97;&#x6CD5;&#x63CF;&#x8FF0;</a></h3>

<table>
<thead>
<tr>
<th style="text-align:center">&#x8F93;&#x5165;&#x53C2;&#x6570;</th>
<th style="text-align:center">&#x4F4D;&#x957F;&#x5EA6;</th>
<th style="text-align:center">&#x9644;&#x6CE8;</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">COUNT</td>
<td style="text-align:center">32</td>
<td style="text-align:center">&#x8BA1;&#x6570;&#x5668;</td>
</tr>
<tr>
<td style="text-align:center">BEARER</td>
<td style="text-align:center">5</td>
<td style="text-align:center">&#x627F;&#x8F7D;&#x5C42;&#x6807;&#x8BC6;</td>
</tr>
<tr>
<td style="text-align:center">DIRECTION</td>
<td style="text-align:center">1</td>
<td style="text-align:center">&#x4F20;&#x8F93;&#x65B9;&#x5411;&#x6807;&#x8BC6;</td>
</tr>
<tr>
<td style="text-align:center">CK</td>
<td style="text-align:center">128</td>
<td style="text-align:center">&#x5B8C;&#x6574;&#x6027;&#x5BC6;&#x94A5;</td>
</tr>
<tr>
<td style="text-align:center">LENGTH</td>
<td style="text-align:center">32</td>
<td style="text-align:center">&#x660E;&#x6587;&#x6D88;&#x606F;&#x6D41;&#x7684;&#x4F4D;&#x957F;&#x5EA6;</td>
</tr>
<tr>
<td style="text-align:center">M</td>
<td style="text-align:center">LENGTH</td>
<td style="text-align:center">&#x8F93;&#x5165;&#x6BD4;&#x7279;&#x6D41;</td>
</tr>
</tbody>
</table>
<table>
<thead>
<tr>
<th style="text-align:center">&#x8F93;&#x51FA;&#x53C2;&#x6570;</th>
<th style="text-align:center">&#x4F4D;&#x957F;&#x5EA6;</th>
<th style="text-align:center">&#x9644;&#x6CE8;</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">MAC</td>
<td style="text-align:center">32</td>
<td style="text-align:center">&#x6D88;&#x606F;&#x8BA4;&#x8BC1;&#x7801;</td>
</tr>
</tbody>
</table>
<h3 class="mume-header" id="zucmac%E5%88%9D%E5%A7%8B%E5%8C%96toc"><a href="#toc">ZUCMac&#x521D;&#x59CB;&#x5316;</a></h3>

<ul>
<li><span class="mathjax-exps">$CK = CK[0] || CK[1] || \dots || CK[15], bitslen(CK[i])=8, i \in [0,15]$</span>;</li>
<li><span class="mathjax-exps">$KEY[i] = CK[i], i\in [0, 15]$</span>;</li>
<li><span class="mathjax-exps">$COUNT = COUNT[0] || COUNT[1] || COUNT[2] || COUNT[3], bitslen(COUNT[i])=8, i \in [0,3]$</span>;</li>
<li><span class="mathjax-exps">$IV = IV[0] || IV[1] ||\dots || IV[15], bitslen(IV[i])=8, i\in [0,15]$</span>;</li>
<li><span class="mathjax-exps">$IV[i] = COUNT[i], i = 0\dots 3$</span>;</li>
<li><span class="mathjax-exps">$IV[4]=BEARER || 0 || 0||0$</span>;</li>
<li><span class="mathjax-exps">$IV[5]=IV[6] = IV[7] = 0x00$</span>;</li>
<li><span class="mathjax-exps">$IV[8]= IV[0]\oplus (DIRECTION \ll 7)$</span>;</li>
<li><span class="mathjax-exps">$IV[9] = IV[1]$</span>;</li>
<li><span class="mathjax-exps">$IV[j+8]=IV[j], j\in [2,5]$</span>;</li>
<li><span class="mathjax-exps">$IV[14] = IV[6] \oplus (DIRECTION \ll 7)$</span>;</li>
<li><span class="mathjax-exps">$IV[15] = IV[7]$</span>;</li>
</ul>
<h3 class="mume-header" id="zucmac%E5%AF%86%E9%92%A5%E6%B5%81%E7%94%9F%E6%88%90toc"><a href="#toc">ZUCMac&#x5BC6;&#x94A5;&#x6D41;&#x751F;&#x6210;</a></h3>

<ul>
<li><span class="mathjax-exps">$n= \lceil LENGTH / 32 \rceil + 2$</span>;</li>
<li><span class="mathjax-exps">$K&apos; = ZUC(KEY,IV,n)$</span>;</li>
<li><span class="mathjax-exps">$K&apos; = k_0 || k_1 || \dots || K_{32\cdot n - 1}, bitslen(k_i)=1, i\in [0, 32\cdot n - 1]$</span>;</li>
<li><span class="mathjax-exps">$k_{i}^{&apos;} = k_i || k_{i+1} || \dots || k_{i+31}, i\in [0,32\cdot n - 1], bitslen(k_{i}^{&apos;})=32$</span>;</li>
</ul>
<h3 class="mume-header" id="zucmac%E6%B6%88%E6%81%AF%E8%AE%A4%E8%AF%81%E7%A0%81%E7%94%9F%E6%88%90toc"><a href="#toc">ZUCMac&#x6D88;&#x606F;&#x8BA4;&#x8BC1;&#x7801;&#x751F;&#x6210;</a></h3>

<ul>
<li><span class="mathjax-exps">$T = 0x00000000$</span>;</li>
<li><code>for i in 0..=(LENGTH-1)</code>:
<ul>
<li>if <span class="mathjax-exps">$M[i] = 1$</span>:
<ul>
<li><span class="mathjax-exps">$T = T\oplus k_{i}^{&apos;}$</span>;</li>
</ul>
</li>
</ul>
</li>
<li><span class="mathjax-exps">$T = T\oplus k_{LENGTH}^{&apos;}$</span>;</li>
<li><span class="mathjax-exps">$MAC = T\oplus k_{32*(n-1)}^{&apos;}$</span></li>
</ul>
<h2 class="mume-header" id="%E9%99%84%E5%BD%95toc"><a href="#toc">&#x9644;&#x5F55;</a></h2>

<h3 class="mume-header" id="%E8%AF%B4%E6%98%8Etoc"><a href="#toc">&#x8BF4;&#x660E;</a></h3>

<ul>
<li>ZUC&#x548C;ZUCCipher&#x662F;&#x56FD;&#x6807;&#x7B97;&#x6CD5;;</li>
<li>ZUCMac&#x662F;&#x884C;&#x6807;&#x7B97;&#x6CD5;;</li>
</ul>
<h3 class="mume-header" id="s_0-s_1toc"><a href="#toc"><span class="mathjax-exps">$S_0, S_1$</span></a></h3>

<pre data-role="codeBlock" data-info="Rust" class="language-rust"><span class="token keyword">const</span> S_0<span class="token punctuation">:</span> <span class="token punctuation">[</span>u8<span class="token punctuation">;</span><span class="token number">256</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">[</span>
	<span class="token number">0x3e</span><span class="token punctuation">,</span><span class="token number">0x72</span><span class="token punctuation">,</span><span class="token number">0x5b</span><span class="token punctuation">,</span><span class="token number">0x47</span><span class="token punctuation">,</span><span class="token number">0xca</span><span class="token punctuation">,</span><span class="token number">0xe0</span><span class="token punctuation">,</span><span class="token number">0x00</span><span class="token punctuation">,</span><span class="token number">0x33</span><span class="token punctuation">,</span><span class="token number">0x04</span><span class="token punctuation">,</span><span class="token number">0xd1</span><span class="token punctuation">,</span><span class="token number">0x54</span><span class="token punctuation">,</span><span class="token number">0x98</span><span class="token punctuation">,</span><span class="token number">0x09</span><span class="token punctuation">,</span><span class="token number">0xb9</span><span class="token punctuation">,</span><span class="token number">0x6d</span><span class="token punctuation">,</span><span class="token number">0xcb</span><span class="token punctuation">,</span>
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	<span class="token number">0xbc</span><span class="token punctuation">,</span><span class="token number">0x26</span><span class="token punctuation">,</span><span class="token number">0x95</span><span class="token punctuation">,</span><span class="token number">0x88</span><span class="token punctuation">,</span><span class="token number">0x8a</span><span class="token punctuation">,</span><span class="token number">0xb0</span><span class="token punctuation">,</span><span class="token number">0xa3</span><span class="token punctuation">,</span><span class="token number">0xfb</span><span class="token punctuation">,</span><span class="token number">0xc0</span><span class="token punctuation">,</span><span class="token number">0x18</span><span class="token punctuation">,</span><span class="token number">0x94</span><span class="token punctuation">,</span><span class="token number">0xf2</span><span class="token punctuation">,</span><span class="token number">0xe1</span><span class="token punctuation">,</span><span class="token number">0xe5</span><span class="token punctuation">,</span><span class="token number">0xe9</span><span class="token punctuation">,</span><span class="token number">0x5d</span><span class="token punctuation">,</span>
	<span class="token number">0xd0</span><span class="token punctuation">,</span><span class="token number">0xdc</span><span class="token punctuation">,</span><span class="token number">0x11</span><span class="token punctuation">,</span><span class="token number">0x66</span><span class="token punctuation">,</span><span class="token number">0x64</span><span class="token punctuation">,</span><span class="token number">0x5c</span><span class="token punctuation">,</span><span class="token number">0xec</span><span class="token punctuation">,</span><span class="token number">0x59</span><span class="token punctuation">,</span><span class="token number">0x42</span><span class="token punctuation">,</span><span class="token number">0x75</span><span class="token punctuation">,</span><span class="token number">0x12</span><span class="token punctuation">,</span><span class="token number">0xf5</span><span class="token punctuation">,</span><span class="token number">0x74</span><span class="token punctuation">,</span><span class="token number">0x9c</span><span class="token punctuation">,</span><span class="token number">0xaa</span><span class="token punctuation">,</span><span class="token number">0x23</span><span class="token punctuation">,</span>
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<span class="token punctuation">]</span><span class="token punctuation">;</span>

<span class="token keyword">const</span> S_1<span class="token punctuation">:</span> <span class="token punctuation">[</span>u8<span class="token punctuation">;</span><span class="token number">256</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">[</span>
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	<span class="token number">0x3a</span><span class="token punctuation">,</span><span class="token number">0xb5</span><span class="token punctuation">,</span><span class="token number">0x56</span><span class="token punctuation">,</span><span class="token number">0x2a</span><span class="token punctuation">,</span><span class="token number">0xc0</span><span class="token punctuation">,</span><span class="token number">0x6d</span><span class="token punctuation">,</span><span class="token number">0xb3</span><span class="token punctuation">,</span><span class="token number">0x05</span><span class="token punctuation">,</span><span class="token number">0x22</span><span class="token punctuation">,</span><span class="token number">0x66</span><span class="token punctuation">,</span><span class="token number">0xbf</span><span class="token punctuation">,</span><span class="token number">0xdc</span><span class="token punctuation">,</span><span class="token number">0x0b</span><span class="token punctuation">,</span><span class="token number">0xfa</span><span class="token punctuation">,</span><span class="token number">0x62</span><span class="token punctuation">,</span><span class="token number">0x48</span><span class="token punctuation">,</span>
	<span class="token number">0xdd</span><span class="token punctuation">,</span><span class="token number">0x20</span><span class="token punctuation">,</span><span class="token number">0x11</span><span class="token punctuation">,</span><span class="token number">0x06</span><span class="token punctuation">,</span><span class="token number">0x36</span><span class="token punctuation">,</span><span class="token number">0xc9</span><span class="token punctuation">,</span><span class="token number">0xc1</span><span class="token punctuation">,</span><span class="token number">0xcf</span><span class="token punctuation">,</span><span class="token number">0xf6</span><span class="token punctuation">,</span><span class="token number">0x27</span><span class="token punctuation">,</span><span class="token number">0x52</span><span class="token punctuation">,</span><span class="token number">0xbb</span><span class="token punctuation">,</span><span class="token number">0x69</span><span class="token punctuation">,</span><span class="token number">0xf5</span><span class="token punctuation">,</span><span class="token number">0xd4</span><span class="token punctuation">,</span><span class="token number">0x87</span><span class="token punctuation">,</span>
	<span class="token number">0x7f</span><span class="token punctuation">,</span><span class="token number">0x84</span><span class="token punctuation">,</span><span class="token number">0x4c</span><span class="token punctuation">,</span><span class="token number">0xd2</span><span class="token punctuation">,</span><span class="token number">0x9c</span><span class="token punctuation">,</span><span class="token number">0x57</span><span class="token punctuation">,</span><span class="token number">0xa4</span><span class="token punctuation">,</span><span class="token number">0xbc</span><span class="token punctuation">,</span><span class="token number">0x4f</span><span class="token punctuation">,</span><span class="token number">0x9a</span><span class="token punctuation">,</span><span class="token number">0xdf</span><span class="token punctuation">,</span><span class="token number">0xfe</span><span class="token punctuation">,</span><span class="token number">0xd6</span><span class="token punctuation">,</span><span class="token number">0x8d</span><span class="token punctuation">,</span><span class="token number">0x7a</span><span class="token punctuation">,</span><span class="token number">0xeb</span><span class="token punctuation">,</span>
	<span class="token number">0x2b</span><span class="token punctuation">,</span><span class="token number">0x53</span><span class="token punctuation">,</span><span class="token number">0xd8</span><span class="token punctuation">,</span><span class="token number">0x5c</span><span class="token punctuation">,</span><span class="token number">0xa1</span><span class="token punctuation">,</span><span class="token number">0x14</span><span class="token punctuation">,</span><span class="token number">0x17</span><span class="token punctuation">,</span><span class="token number">0xfb</span><span class="token punctuation">,</span><span class="token number">0x23</span><span class="token punctuation">,</span><span class="token number">0xd5</span><span class="token punctuation">,</span><span class="token number">0x7d</span><span class="token punctuation">,</span><span class="token number">0x30</span><span class="token punctuation">,</span><span class="token number">0x67</span><span class="token punctuation">,</span><span class="token number">0x73</span><span class="token punctuation">,</span><span class="token number">0x08</span><span class="token punctuation">,</span><span class="token number">0x09</span><span class="token punctuation">,</span>
	<span class="token number">0xee</span><span class="token punctuation">,</span><span class="token number">0xb7</span><span class="token punctuation">,</span><span class="token number">0x70</span><span class="token punctuation">,</span><span class="token number">0x3f</span><span class="token punctuation">,</span><span class="token number">0x61</span><span class="token punctuation">,</span><span class="token number">0xb2</span><span class="token punctuation">,</span><span class="token number">0x19</span><span class="token punctuation">,</span><span class="token number">0x8e</span><span class="token punctuation">,</span><span class="token number">0x4e</span><span class="token punctuation">,</span><span class="token number">0xe5</span><span class="token punctuation">,</span><span class="token number">0x4b</span><span class="token punctuation">,</span><span class="token number">0x93</span><span class="token punctuation">,</span><span class="token number">0x8f</span><span class="token punctuation">,</span><span class="token number">0x5d</span><span class="token punctuation">,</span><span class="token number">0xdb</span><span class="token punctuation">,</span><span class="token number">0xa9</span><span class="token punctuation">,</span>
	<span class="token number">0xad</span><span class="token punctuation">,</span><span class="token number">0xf1</span><span class="token punctuation">,</span><span class="token number">0xae</span><span class="token punctuation">,</span><span class="token number">0x2e</span><span class="token punctuation">,</span><span class="token number">0xcb</span><span class="token punctuation">,</span><span class="token number">0x0d</span><span class="token punctuation">,</span><span class="token number">0xfc</span><span class="token punctuation">,</span><span class="token number">0xf4</span><span class="token punctuation">,</span><span class="token number">0x2d</span><span class="token punctuation">,</span><span class="token number">0x46</span><span class="token punctuation">,</span><span class="token number">0x6e</span><span class="token punctuation">,</span><span class="token number">0x1d</span><span class="token punctuation">,</span><span class="token number">0x97</span><span class="token punctuation">,</span><span class="token number">0xe8</span><span class="token punctuation">,</span><span class="token number">0xd1</span><span class="token punctuation">,</span><span class="token number">0xe9</span><span class="token punctuation">,</span>
	<span class="token number">0x4d</span><span class="token punctuation">,</span><span class="token number">0x37</span><span class="token punctuation">,</span><span class="token number">0xa5</span><span class="token punctuation">,</span><span class="token number">0x75</span><span class="token punctuation">,</span><span class="token number">0x5e</span><span class="token punctuation">,</span><span class="token number">0x83</span><span class="token punctuation">,</span><span class="token number">0x9e</span><span class="token punctuation">,</span><span class="token number">0xab</span><span class="token punctuation">,</span><span class="token number">0x82</span><span class="token punctuation">,</span><span class="token number">0x9d</span><span class="token punctuation">,</span><span class="token number">0xb9</span><span class="token punctuation">,</span><span class="token number">0x1c</span><span class="token punctuation">,</span><span class="token number">0xe0</span><span class="token punctuation">,</span><span class="token number">0xcd</span><span class="token punctuation">,</span><span class="token number">0x49</span><span class="token punctuation">,</span><span class="token number">0x89</span><span class="token punctuation">,</span>
	<span class="token number">0x01</span><span class="token punctuation">,</span><span class="token number">0xb6</span><span class="token punctuation">,</span><span class="token number">0xbd</span><span class="token punctuation">,</span><span class="token number">0x58</span><span class="token punctuation">,</span><span class="token number">0x24</span><span class="token punctuation">,</span><span class="token number">0xa2</span><span class="token punctuation">,</span><span class="token number">0x5f</span><span class="token punctuation">,</span><span class="token number">0x38</span><span class="token punctuation">,</span><span class="token number">0x78</span><span class="token punctuation">,</span><span class="token number">0x99</span><span class="token punctuation">,</span><span class="token number">0x15</span><span class="token punctuation">,</span><span class="token number">0x90</span><span class="token punctuation">,</span><span class="token number">0x50</span><span class="token punctuation">,</span><span class="token number">0xb8</span><span class="token punctuation">,</span><span class="token number">0x95</span><span class="token punctuation">,</span><span class="token number">0xe4</span><span class="token punctuation">,</span>
	<span class="token number">0xd0</span><span class="token punctuation">,</span><span class="token number">0x91</span><span class="token punctuation">,</span><span class="token number">0xc7</span><span class="token punctuation">,</span><span class="token number">0xce</span><span class="token punctuation">,</span><span class="token number">0xed</span><span class="token punctuation">,</span><span class="token number">0x0f</span><span class="token punctuation">,</span><span class="token number">0xb4</span><span class="token punctuation">,</span><span class="token number">0x6f</span><span class="token punctuation">,</span><span class="token number">0xa0</span><span class="token punctuation">,</span><span class="token number">0xcc</span><span class="token punctuation">,</span><span class="token number">0xf0</span><span class="token punctuation">,</span><span class="token number">0x02</span><span class="token punctuation">,</span><span class="token number">0x4a</span><span class="token punctuation">,</span><span class="token number">0x79</span><span class="token punctuation">,</span><span class="token number">0xc3</span><span class="token punctuation">,</span><span class="token number">0xde</span><span class="token punctuation">,</span>
	<span class="token number">0xa3</span><span class="token punctuation">,</span><span class="token number">0xef</span><span class="token punctuation">,</span><span class="token number">0xea</span><span class="token punctuation">,</span><span class="token number">0x51</span><span class="token punctuation">,</span><span class="token number">0xe6</span><span class="token punctuation">,</span><span class="token number">0x6b</span><span class="token punctuation">,</span><span class="token number">0x18</span><span class="token punctuation">,</span><span class="token number">0xec</span><span class="token punctuation">,</span><span class="token number">0x1b</span><span class="token punctuation">,</span><span class="token number">0x2c</span><span class="token punctuation">,</span><span class="token number">0x80</span><span class="token punctuation">,</span><span class="token number">0xf7</span><span class="token punctuation">,</span><span class="token number">0x74</span><span class="token punctuation">,</span><span class="token number">0xe7</span><span class="token punctuation">,</span><span class="token number">0xff</span><span class="token punctuation">,</span><span class="token number">0x21</span><span class="token punctuation">,</span>
	<span class="token number">0x5a</span><span class="token punctuation">,</span><span class="token number">0x6a</span><span class="token punctuation">,</span><span class="token number">0x54</span><span class="token punctuation">,</span><span class="token number">0x1e</span><span class="token punctuation">,</span><span class="token number">0x41</span><span class="token punctuation">,</span><span class="token number">0x31</span><span class="token punctuation">,</span><span class="token number">0x92</span><span class="token punctuation">,</span><span class="token number">0x35</span><span class="token punctuation">,</span><span class="token number">0xc4</span><span class="token punctuation">,</span><span class="token number">0x33</span><span class="token punctuation">,</span><span class="token number">0x07</span><span class="token punctuation">,</span><span class="token number">0x0a</span><span class="token punctuation">,</span><span class="token number">0xba</span><span class="token punctuation">,</span><span class="token number">0x7e</span><span class="token punctuation">,</span><span class="token number">0x0e</span><span class="token punctuation">,</span><span class="token number">0x34</span><span class="token punctuation">,</span>
	<span class="token number">0x88</span><span class="token punctuation">,</span><span class="token number">0xb1</span><span class="token punctuation">,</span><span class="token number">0x98</span><span class="token punctuation">,</span><span class="token number">0x7c</span><span class="token punctuation">,</span><span class="token number">0xf3</span><span class="token punctuation">,</span><span class="token number">0x3d</span><span class="token punctuation">,</span><span class="token number">0x60</span><span class="token punctuation">,</span><span class="token number">0x6c</span><span class="token punctuation">,</span><span class="token number">0x7b</span><span class="token punctuation">,</span><span class="token number">0xca</span><span class="token punctuation">,</span><span class="token number">0xd3</span><span class="token punctuation">,</span><span class="token number">0x1f</span><span class="token punctuation">,</span><span class="token number">0x32</span><span class="token punctuation">,</span><span class="token number">0x65</span><span class="token punctuation">,</span><span class="token number">0x04</span><span class="token punctuation">,</span><span class="token number">0x28</span><span class="token punctuation">,</span>
	<span class="token number">0x64</span><span class="token punctuation">,</span><span class="token number">0xbe</span><span class="token punctuation">,</span><span class="token number">0x85</span><span class="token punctuation">,</span><span class="token number">0x9b</span><span class="token punctuation">,</span><span class="token number">0x2f</span><span class="token punctuation">,</span><span class="token number">0x59</span><span class="token punctuation">,</span><span class="token number">0x8a</span><span class="token punctuation">,</span><span class="token number">0xd7</span><span class="token punctuation">,</span><span class="token number">0xb0</span><span class="token punctuation">,</span><span class="token number">0x25</span><span class="token punctuation">,</span><span class="token number">0xac</span><span class="token punctuation">,</span><span class="token number">0xaf</span><span class="token punctuation">,</span><span class="token number">0x12</span><span class="token punctuation">,</span><span class="token number">0x03</span><span class="token punctuation">,</span><span class="token number">0xe2</span><span class="token punctuation">,</span><span class="token number">0xf2</span><span class="token punctuation">,</span>

<span class="token punctuation">]</span><span class="token punctuation">;</span>
</pre><h3 class="mume-header" id="kdtoc"><a href="#toc">KD</a></h3>

<pre data-role="codeBlock" data-info="Rust" class="language-rust"><span class="token keyword">const</span> KD<span class="token punctuation">:</span> <span class="token punctuation">[</span>u16<span class="token punctuation">;</span><span class="token number">16</span><span class="token punctuation">]</span> <span class="token operator">=</span> <span class="token punctuation">[</span>
	<span class="token number">0x44D7</span><span class="token punctuation">,</span><span class="token number">0x26BC</span><span class="token punctuation">,</span><span class="token number">0x626B</span><span class="token punctuation">,</span><span class="token number">0x135E</span><span class="token punctuation">,</span><span class="token number">0x5789</span><span class="token punctuation">,</span><span class="token number">0x35E2</span><span class="token punctuation">,</span><span class="token number">0x7135</span><span class="token punctuation">,</span><span class="token number">0x09AF</span><span class="token punctuation">,</span>
	<span class="token number">0x4D78</span><span class="token punctuation">,</span><span class="token number">0x2F13</span><span class="token punctuation">,</span><span class="token number">0x6BC4</span><span class="token punctuation">,</span><span class="token number">0x1AF1</span><span class="token punctuation">,</span><span class="token number">0x5E26</span><span class="token punctuation">,</span><span class="token number">0x3C4D</span><span class="token punctuation">,</span><span class="token number">0x789A</span><span class="token punctuation">,</span><span class="token number">0x47AC</span><span class="token punctuation">,</span>

<span class="token punctuation">]</span><span class="token punctuation">;</span>
</pre><h2 class="mume-header" id="%E5%8F%82%E8%80%83%E8%B5%84%E6%96%99">&#x53C2;&#x8003;&#x8D44;&#x6599;</h2>

<ul>
<li>GM/T 0001-2012 &#x7956;&#x51B2;&#x4E4B;&#x5E8F;&#x5217;&#x5BC6;&#x7801;&#x7B97;&#x6CD5;;</li>
</ul>

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